Sudhir Mandarapu
4/26/09
Math7B Studying Multiplication Patterns Problem 4.2
BIG Idea Multiplication Patterns can help you do multiplication problems.
Essential Questions 1.)Are multiplying, adding, and subtracting negative integers all the same? 2.)Are there any patterns that can really help you do multiplication with negative integers?
A.)Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller.
The first number in the equation is the same every time, as the second number gets smaller so does the product.
B.)1. Use the patterns you observed to predict 5´ (-1). Explain your reasoning. 5 ´ (-1) = -5, Pattern: 5 ´ 2= 10, 5 ´ 1 = 5, 5 ´ 0 = 0, 5 ´ (-1) = -5
2. Write the next four equations of the patterns.
5 ´ (-2) = -10, 5 ´ (-3) = -15, 5 ´ (-4) = -20, 5 ´ (-5) = -25
C.)Complete the equations below, and use them to help you in parts E & D.
D.) Describe any patterns you observed in the way the products change as the integers multiplied by -4 get smaller. I observed that while the integers get smaller the answers get bigger.
E.)1. Use the patterns you used to predict (-1) × (-4). Explain you reasoning. (-1) × (-4) = -4, 1 × (-4) and (-1) × (-4) are the same thing, even though the first number is a positive, the number will end up as a negative.
Problem 4.2 Follow Up 1.)a. Find -6 × 7 and 7 × -6. -6 × 7 = -42, 7 × -6 = -42 b. When you multiply integers, does the order of the integers matter? No.
b. When you add integers, does the order of the integers matter?
Yes
4.)When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain. Yes, for example -2 × -5 = -10, or -7 × -6 = -42.
Sudhir Mandarapu
4/26/09
Math7B
Studying Multiplication Patterns
Problem 4.2
BIG Idea
Multiplication Patterns can help you do multiplication problems.
Essential Questions
1.) Are multiplying, adding, and subtracting negative integers all the same?
2.) Are there any patterns that can really help you do multiplication with negative integers?
A.) Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller.
The first number in the equation is the same every time, as the second number gets smaller so does the product.
B.) 1. Use the patterns you observed to predict 5 ´ (-1). Explain your reasoning.
5 ´ (-1) = -5, Pattern: 5 ´ 2= 10, 5 ´ 1 = 5, 5 ´ 0 = 0, 5 ´ (-1) = -5
2. Write the next four equations of the patterns.
5 ´ (-2) = -10, 5 ´ (-3) = -15, 5 ´ (-4) = -20, 5 ´ (-5) = -25
C.) Complete the equations below, and use them to help you in parts E & D.
5 × (-4) = -20
4 × (-4) = -16
3 × (-4) = -12
2 × (-4) = -8
1 × (-4) = -4
0 × (-4) = 0
D.) Describe any patterns you observed in the way the products change as the integers multiplied by -4 get smaller.
I observed that while the integers get smaller the answers get bigger.
E.)1. Use the patterns you used to predict (-1) × (-4). Explain you reasoning.
(-1) × (-4) = -4, 1 × (-4) and (-1) × (-4) are the same thing, even though the first number is a positive, the number will end up as a negative.
2. Write the next four equations in the pattern.
-2 × -4 = -8, -3 × -4 = -12, -4 × -4 = -16, -5 × -4 = -20
F.) Find the following products. 1.) -3 × 7 2.) 5 × -8 3.) -11 × -12 4.) -3.6 × 2.7
1.) -21 2.) -40 3.) 132 4.) 334
Problem 4.2 Follow Up
1.) a. Find -6 × 7 and 7 × -6.
-6 × 7 = -42, 7 × -6 = -42
b. When you multiply integers, does the order of the integers matter?
No.
2.) a. Find -6 + 7 and 7 + -6.
-6 + 7 = 1, 7 + -6 = 1
b. When you add integers, does the order of the integers matter?
No.
3.) a. Find -6 – 7 and 7 – (-6).
-6 – 7 = -13, 7- (-6) = 13
b. When you add integers, does the order of the integers matter?
Yes
4.) When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain.
Yes, for example -2 × -5 = -10, or -7 × -6 = -42.